We propose an active plasmonic device based on graphene. By using a diffractive grating on silicon, highly confined plasmonic waves in monolayer graphene are efficiently excited. The high electric field of the surface plasmons near the graphene layer makes them ideal for use in biosensors, where a very small change in refractive index should be detected. A small change in the refractive index of surroundings medium, induces a large change in resonant wavelength. The spectral shift per refractive index unit (∆λ0/RIU) of the sensor is considerable and exceeding 2000 nm/RIU with a narrow line width spectral of the plasmon resonances. The figure of merit for this sensor is approximately equal to 14.2 and electrical tuning can be achieved by adjusting the Fermi level in graphene. Therefore, this grating plasmonic structure is highly sensitive and can be used in high resolution biosensing applications.